Question 0121

Equations and Inequalities
2021 Paper 1 Question 1 Variant

Question

A function f{f} is defined by f(x)=ax3+bx2+cx+d.{f(x)=ax^3+bx^2+cx+d.} The graph of y=f(x){y=f(x)} passes through the points (1,11){(1, - 11)} and (2,21).{(2, 21).} The graph has a turning point at x=1,{x=1,} and 01f(x)  dx=5.{\displaystyle \int_0^1 f(x) \; \mathrm{d}x = - 5.}
Find the values of a,b,c{a,b,c} and d.{d.}
[5]

Answer